I have been exploring multilevel structural equation modeling (MSEM) option for my research. What I don't understand is how to do cross-level analysis using MSEM (with Mplus).

In HLM, the DV is always at the lowest level. But in MSEM as far as i understand, all i can do is run SEM analysis at between and within levels. But it is not possible to regress a predictor at one level to the DV on another.

1) If my understanding is not correct, can i be guided to some resources which explain how to do the cross-level MSEM analysis using Mplus.

2) if the cross-level analysis is possible in MSEM done in Mplus, is it like HLM where DV is at lowest level

There are no such limitations on MSEM in Mplus. In fact, Mplus is considerably more general in this regard than conventional HLM. There are several examples in the User's Guide chapter 9 (available on our web site) which show you how this works. DVs can be on level 1 or level 2, or both.

Dear Mplus team, I'd like to resume the question about cross-level analysis using MSEM. When I did HLM, the independent variables(between continuous variable) should be standardized.But in Mplus, I found this will be wrong.Mplus output show "THE ESTIMATED WITHIN COVARIANCE MATRIX IS NOT POSITIVE DEFINITE AS IT SHOULD BE. COMPUTATION COULD NOT BE COMPLETED. THE VARIANCE OF GENDER APPROACHES 0. FIX THIS VARIANCE AND THE CORRESPONDING COVARIANCES TO 0, DECREASE THE MINIMUM VARIANCE, OR SPECIFY THE VARIABLE AS A BETWEEN VARIABLE." I wonder if it don't need to standardize the between continuous indepent variables in Mplus? but I really think that the between independent variables should be standardized, for we use different scale or questionnaire to get the independent variable value( usually the sum of items),and the different scale has different number of item.

I'm a little confused. Gender is not a continuous variable. It does not seem standardization is your problem. I suggest doing a TYPE=BASIC on the non-standardized variables to see if you are reading your data correctly.